Chapter 10 - Systems of Equations and Inequalities - Section 10.6 Systems of Nonlinear Equations - 10.6 Assess Your Understanding - Page 795: 72

$(5,2)$

1. Let the two numbers be $x, y$, based on the given conditions, we can get: $\begin{cases} x+y=7 \\ x^2-y^2=21 \end{cases}$ 2. The 1st equation gives $y=7-x$, use it in the 2nd equation to get $x^2-x^2+14x-49=21$ or $14x=70$ thus $x=5$ 3. Use the 1st equation again to get the solution(s) $(5,2)$